📝 Reading and writing decimals (28 MCQs)

📖 From Digital SAT Algebra • 1. Basics of Algebra • 28 questions available

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What is Reading and writing decimals?

Definition:
Reading and writing decimals involves interpreting the place value of digits after the decimal point, where each position represents a fraction with denominator a power of ten (tenths, hundredths, thousandths, etc.), and expressing the decimal in words or as a fraction, and vice versa.

Working:
To read a decimal, say the whole number part, then 'and' for the decimal point, then the fractional part as a whole number followed by the place value name of the last digit (e.g., $0.34$ is 'thirty-four hundredths'); to write, place digits in their corresponding place values.

Example:
Write $0.205$ in words and as a fraction.
Solution: In words: 'two hundred five thousandths'; as fraction: $\frac{205}{1000} = \frac{41}{200}$ .

Reason:
This skill is necessary for interpreting numerical data, making conversions, and ensuring accurate communication of decimal quantities in algebra, science, and everyday life, such as in measurements and currency.

Easy

Medium

Hard

📝 All Reading and writing decimals MCQs

Q1. A student writes the decimal $4.070$ in words as “four and seventy hundredths.” Which explanation best identifies the error and gives the correct wording?

A.The zero in the tenths place is ignored; the correct wording is four and seven tenths.

B.The zero in the hundredths place is ignored; the correct wording is four and seven hundredths. ✅

C.The zero in the tenths place changes the place value of 7; the correct wording is four and seventy thousandths.

D.The final zero is irrelevant, so the correct wording is four and seventy tenths.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The digit 7 is in the hundredths place because the tenths position contains 0. Therefore, $4.070$ is correctly named four and seventy hundredths. The zero preserves the place-value structure.

Q2. A measurement is recorded as “eight and six hundredths.” A student writes $8.6$ . Another writes $8.06$ . Which representation correctly matches the words, and why?

8.6

, because 6 is always in the tenths place.

8.60

, because hundredths require two digits after the decimal point.

8.06

, because 6 must occupy the hundredths place. ✅

8.006

, because the word hundredths requires three decimal places.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The word hundredths identifies the second digit after the decimal point. Thus, six hundredths is $0.06$ , making the complete decimal $8.06$ . Writing $8.6$ incorrectly places 6 in the tenths position.

Q3. A shop label says “three and forty-five hundredths” for a price adjustment. Which decimal should the cashier enter if the system requires the exact place value represented by the words?

A.3.045

B.3.45 ✅

C.3.405

D.34.5

💡 Difficulty: easy | ✅ Correct: B

📖 Explanation: “Three and forty-five hundredths” means three plus forty-five hundredths. Since $45$ occupies the two decimal places representing hundredths, the number is $3.45$ , not $3.045$ or $3.405$ .

Q4. A number-line segment from 2 to 3 is divided into 100 equal parts. A point is located 7 small divisions after 2. Which decimal and verbal name describe the point?

2.7

, two and seven tenths

2.07

, two and seven hundredths ✅

2.007

, two and seven thousandths

2.70

, two and seventy hundredths only

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Dividing the interval from 2 to 3 into 100 equal parts makes each division one hundredth. Seven divisions after 2 therefore represent $2.07$ , which is named two and seven hundredths.

Q5. Two students convert the words “five and nine tenths” into decimals. Ali writes $5.09$ , while Sara writes $5.9$ . Who is correct, and what misconception explains the other answer?

A.Ali is correct because every decimal must contain two digits.

B.Sara is correct because nine tenths places 9 in the tenths position; Ali confused tenths with hundredths. ✅

C.Both are correct because

5.09=5.9

D.Ali is correct because 9 tenths means 9 hundredths.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Sara is correct because tenths are represented by the first digit after the decimal point, giving $5.9$ . Ali incorrectly placed 9 in the hundredths position, changing the value to five and nine hundredths.

Q6. A number-line diagram marks a point exactly halfway between $6.2$ and $6.3$ . A student names it “six and twenty-five hundredths.” Which decimal should be written, and what reasoning supports it?

6.025

, because the point is halfway

6.25

, because 25 is halfway between 20 and 30 hundredths ✅

6.205

, because 5 is halfway between 0 and 10

6.5

, because halfway means adding five tenths

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The interval from $6.2$ to $6.3$ can be written as $6.20$ to $6.30$ . The midpoint is $6.25$ , or twenty-five hundredths, because 25 lies halfway between 20 and 30.

Q7. A teacher asks for a decimal whose name is “nine and four hundredths.” A student claims $9.4$ works because the digit 4 appears after the decimal point. Which response best evaluates the claim?

A.Correct, because any digit after the decimal represents hundredths.

B.Correct, because

9.4

and

9.04

have the same value.

C.Incorrect, because

9.4

means nine and four tenths; the required decimal is

9.04

. ✅

D.Incorrect, because hundredths cannot be represented using a zero.

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The student's reasoning ignores place value. In $9.4$ , the 4 is in the tenths place. To represent four hundredths, a zero must occupy the tenths place, producing $9.04$ .

Q8. In the decimal $7.406$ , which statement correctly identifies the value of the digit $4$ and explains its position?

A.The 4 has value

4

because it is the first digit after the decimal.

B.The 4 has value

0.4

because it is in the tenths place. ✅

C.The 4 has value

0.04

because it is in the hundredths place.

D.The 4 has value

0.004

because it is in the thousandths place.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The first digit after the decimal point represents tenths. Therefore, the 4 in $7.406$ represents $4$ tenths, or $0.4$ . The surrounding zeros do not change its place value.

Q9. A science instrument records $12.305$ liters. A student says the 3 represents three hundredths because there are two digits after it. Which evaluation is correct?

A.The student is correct because 3 is always hundredths in a decimal.

B.The student is incorrect because 3 is in the tenths place and represents

0.3

. ✅

C.The student is incorrect because 3 represents

3

thousandths.

D.The student is correct because

0.03

is equivalent to

0.3

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: In $12.305$ , the first digit after the decimal is 3, so it occupies the tenths place and has value $0.3$ . The later digits do not determine the place of an earlier digit.

Q10. A factory measures two objects as $5.070$ kg and $5.007$ kg. Which statement correctly compares the value of the 7 in each measurement?

A.The 7 has the same value in both measurements because both numbers contain 7.

B.The first 7 represents

7

tenths, while the second represents

7

hundredths.

C.The first 7 represents

7

hundredths, while the second represents

7

thousandths. ✅

D.The first 7 represents

7

thousandths, while the second represents

7

hundredths.

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: In $5.070$ , the 7 is in the hundredths place, so its value is $0.07$ . In $5.007$ , the 7 is in the thousandths place, so its value is $0.007$ .

Q11. A number line from $3$ to $4$ is divided into 100 equal intervals. A point is located 62 intervals after $3$ . Which decimal represents the point?

A.3.62 ✅

B.3.062

C.3.602

D.3.26

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The whole interval from 3 to 4 represents one unit and is divided into 100 equal parts, so each part is one hundredth. Sixty-two intervals therefore give $3.62$ .

Q12. A student claims that in $8.909$ , the two 9s have equal values because they are the same digit. Which response best analyzes the claim?

A.Correct, because identical digits always have identical values.

B.Correct, because both 9s are to the right of the decimal.

C.Incorrect, because the first 9 is worth

0.9

, while the second is worth

0.009

. ✅

D.Incorrect, because the first 9 is worth

9

and the second is worth

0.09

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: A digit's value depends on its position. In $8.909$ , the first 9 is in the tenths place and equals $0.9$ , while the second 9 is in the thousandths place and equals $0.009$ .

Q13. A digital scale displays $24.508$ kg. The technician wants to increase the measurement by exactly $0.04$ kg without changing any other intended place value. What should the new reading be?

A.24.548 ✅

B.24.512

C.24.908

D.28.508

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: The amount $0.04$ is four hundredths, so it must be added to the hundredths place. Adding $0.040$ to $24.508$ gives $24.548$ , while the thousandths digit remains unchanged.

Q14. A puzzle asks for a decimal between $6.4$ and $6.5$ in which the digit 7 has a value of $0.007$ . Which number satisfies both conditions?

A.6.47

B.6.407 ✅

C.6.704

D.6.047

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: A value of $0.007$ places 7 in the thousandths position. The number must also lie between $6.4$ and $6.5$ . Only $6.407$ satisfies both requirements because it is slightly greater than $6.400$ .

Q15. A teacher asks a student to name $7.035$ in words. Which name correctly preserves the place value of every digit?

A.Seven and thirty-five tenths

B.Seven and three hundredths

C.Seven and thirty-five thousandths ✅

D.Seven and three hundred fifty thousandths

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: The decimal $7.035$ has 3 in the hundredths place and 5 in the thousandths place. Together, the decimal part represents 35 thousandths, so the correct name is seven and thirty-five thousandths.

Q16. A measurement is recorded as $12.408$ meters. A student calls it “twelve and four hundred eight thousandths.” Is the name correct?

A.Yes, because all three decimal digits represent thousandths. ✅

B.No, it should be twelve and forty-eight thousandths.

C.No, it should be twelve and four hundred eight hundredths.

D.Yes, because 408 is always read as hundredths.

💡 Difficulty: medium | ✅ Correct: A

📖 Explanation: The name is correct because three digits follow the decimal point, making the final place thousandths. The digits 408 represent four hundred eight thousandths, while the zero preserves the place-value structure.

Q17. A recipe requires $3.06$ liters of liquid. Which verbal description should appear on a measuring label so that another person interprets the amount correctly?

A.Three and six tenths

B.Three and sixty hundredths

C.Three and six hundredths ✅

D.Three and six thousandths

💡 Difficulty: easy | ✅ Correct: C

📖 Explanation: In $3.06$ , the 0 occupies the tenths place and 6 occupies the hundredths place. Therefore, the decimal portion is six hundredths, making the correct name three and six hundredths.

Q18. Two students name $5.070$ . Ali says “five and seventy hundredths,” while Sara says “five and seventy thousandths.” Which evaluation is mathematically correct?

A.Ali is correct because the final zero can be ignored when naming.

B.Sara is correct because 070 represents seventy thousandths. ✅

C.Both are incorrect because decimals cannot contain zeros.

D.Both are correct because

5.070

has the same value as

5.70

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The decimal $0.070$ represents seventy thousandths, or $0.07$ . Although the trailing zero does not change the numerical value, it does not change the place-value interpretation of the digits. Sara's naming matches the written decimal.

Q19. A point on a number line lies at $4.25$ . A student names it “four and twenty-five tenths.” Which correction best explains the mistake?

A.The decimal should be named four and twenty-five hundredths because 25 occupies two decimal places. ✅

B.The decimal should be named four and two tenths because only the first digit matters.

C.The decimal should be named four and twenty-five thousandths because 25 has two digits.

D.The decimal should be named forty-two and five tenths because the decimal point is ignored.

💡 Difficulty: hard | ✅ Correct: A

📖 Explanation: In $4.25$ , two digits appear after the decimal point, so the decimal part is measured in hundredths. Thus, $0.25$ is twenty-five hundredths, not twenty-five tenths.

Q20. A number-line interval from $2$ to $3$ is divided into 100 equal parts. A marked point is 9 intervals after $2$ . Which name correctly describes the point?

A.Two and nine tenths

B.Two and nine hundredths ✅

C.Two and ninety hundredths

D.Two and nine thousandths

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: Because the interval from 2 to 3 is divided into 100 equal parts, each interval represents one hundredth. Nine intervals after 2 give $2.09$ , which is named two and nine hundredths.

Q21. A puzzle requires a decimal between $8.3$ and $8.4$ whose name contains “twenty-five thousandths.” Which number satisfies the condition?

A.8.025

B.8.205

C.8.325 ✅

D.8.425

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: “Twenty-five thousandths” means $0.025$ . Adding this to $8.3$ , written as $8.300$ , gives $8.325$ . This number is greater than $8.3$ and less than $8.4$ , satisfying both conditions.

Q22. A measurement is described as “six and forty-two hundredths.” Which decimal correctly represents the measurement?

A.6.042

B.6.42 ✅

C.6.402

D.6.42

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The phrase “forty-two hundredths” means $42$ parts out of $100$ , which is $0.42$ . Adding this to 6 gives $6.42$ . The distractors incorrectly shift the digits into thousandths or tenths places.

Q23. A student needs to record “nine and seven thousandths” on a digital form. Which entry preserves the place value stated in the name?

A.9.7

B.9.07

C.9.007 ✅

D.9.07

💡 Difficulty: medium | ✅ Correct: C

📖 Explanation: Seven thousandths is $0.007$ , so the 7 must occupy the thousandths place. The zeros in the tenths and hundredths positions are necessary to hold those place values, giving $9.007$ .

Q24. A package label says “three and eighty hundredths.” A worker enters $3.080$ . What is the best analysis of the worker's entry?

A.It is correct because 80 hundredths requires three decimal places.

B.It is incorrect because

3.080

means three and eighty thousandths; the correct decimal is

3.80

. ✅

C.It is incorrect because the correct decimal must be

3.008

D.It is correct because

3.080

and

3.80

have different place values.

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: Eighty hundredths is $0.80$ , so the decimal is $3.80$ . In $3.080$ , the 80 is interpreted across the hundredths and thousandths positions as eighty thousandths. The worker has shifted the place-value scale.

Q25. A number line from $5$ to $6$ is divided into 100 equal sections. A point is 34 sections after $5$ . Which decimal should be written for the point?

A.5.034

B.5.34 ✅

C.5.304

D.5.43

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The interval from 5 to 6 represents one whole and is divided into 100 equal parts, so each section represents one hundredth. Thirty-four sections therefore represent $34$ hundredths, giving $5.34$ .

Q26. A recipe calls for “two and five hundredths” liters of an ingredient. One student writes $2.5$ , while another writes $2.05$ . Which student correctly converts the name and why?

A.The first student, because 5 after the decimal always means five hundredths.

B.The second student, because the word hundredths requires 5 in the second decimal position. ✅

C.Both students, because

2.5=2.05

D.Neither student, because the decimal must contain three places.

💡 Difficulty: medium | ✅ Correct: B

📖 Explanation: The second student is correct. “Five hundredths” equals $0.05$ , so the required decimal is $2.05$ . Writing $2.5$ places 5 in the tenths position and represents five tenths instead.

Q27. A scientist records a value described as “seven and two hundred three thousandths.” Which decimal should be entered, and what reasoning makes the placement reliable?

A.7.23

B.7.203 ✅

C.7.023

D.7.23

💡 Difficulty: hard | ✅ Correct: B

📖 Explanation: The phrase “two hundred three thousandths” means $203$ thousandths, or $0.203$ . Therefore, combining it with 7 gives $7.203$ . The zero is essential because it keeps 2 in the tenths position.

Q28. A puzzle asks for a decimal greater than $4.5$ but less than $4.6$ , and its name must contain “seventy-five thousandths.” Which choice satisfies both conditions?

A.4.075

B.4.5075

C.4.575 ✅

D.4.75

💡 Difficulty: hard | ✅ Correct: C

📖 Explanation: Seventy-five thousandths is $0.075$ . Writing $4.5$ as $4.500$ and adding $0.075$ gives $4.575$ . This value lies between $4.5$ and $4.6$ , satisfying both the naming and comparison requirements.

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