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Math · Decimals
Decimals as Numbers: Tenths, Hundredths, Compare, Round
Build Grade 4–5 decimal sense by connecting tenths and hundredths to fractions, place value, number lines, comparison and simple rounding.
The idea
Decimals are another way to write parts of one whole. One tenth is 0.1, one hundredth is 0.01, and 0.34 means 3 tenths and 4 hundredths. The decimal point keeps the ones place separate from the fractional places.
Place value matters more than the number of digits. For example, 0.7 = 0.70 because both name seventy hundredths. When comparing decimals, line up place values and compare from left to right.
A number line helps keep decimals meaningful. Values such as 0.42 and 0.47 are not just strings of digits; they are points between 0.4 and 0.5. Rounding asks which benchmark value a number is closer to.
Worked examples
Example 1 · Read the place value
What does 0.36 mean?
- The 3 is in the tenths place, so it represents 3/10.
- The 6 is in the hundredths place, so it represents 6/100.
- Together that is 36/100.
0.36 = 36/100 = 3 tenths + 6 hundredths.
Example 2 · Add a zero without changing value
Are 0.7 and 0.70 equal?
- 0.7 means 7 tenths.
- 7 tenths equals 70 hundredths.
- A trailing zero to the right does not change the value.
Yes. 0.7 = 0.70.
Example 3 · Compare two decimals
Which is larger: 0.58 or 0.6?
- Write 0.6 as 0.60.
- Compare hundredths: 58 hundredths versus 60 hundredths.
- 60 hundredths is larger.
0.6 > 0.58.
Example 4 · Locate a decimal
Where is 0.43 on a number line?
- 0.43 lies between 0.4 and 0.5.
- Think of the interval as 10 hundredths: 0.40, 0.41, ... 0.50.
- 0.43 is 3 hundredths past 0.40.
0.43 is between 0.4 and 0.5, closer to 0.4.
Example 5 · Convert a fraction
Write 27/100 as a decimal.
- The denominator is 100.
- Twenty-seven hundredths places 27 in the hundredths count.
- Write 0.27.
27/100 = 0.27.
Example 6 · Round to the nearest tenth
Round 0.46 to the nearest tenth.
- 0.46 lies between 0.4 and 0.5.
- It is 0.06 above 0.4 and 0.04 below 0.5.
- It is closer to 0.5.
0.46 rounds to 0.5.
Common mistakes
These are tempting because they use familiar operations. Check what the question is actually measuring.
Why this fails: Decimal digits have place value. Rewrite 0.7 as 0.70; then 70 hundredths is greater than 65 hundredths.
Why this fails: A trailing zero to the right of a decimal does not change the value: 0.50 = 0.5.
Why this fails: 0.34 is 3 tenths and 4 hundredths, or 34 hundredths.
Why this fails: Number-line distance explains why the next digit matters and makes rounding easier to check.
Why this fails: The decimal point separates whole-number places from tenths, hundredths and smaller places.
Foundation
Foundation practice
Read tenths and hundredths, connect fractions and decimals, and use equivalent decimal names.
1. What place is the 4 in 0.47?
2. What value does the 7 represent in 0.47?
3. Write 6/10 as a decimal.
4. Write 23/100 as a decimal.
5. Are 0.4 and 0.40 equal?
6. Write 0.08 as a fraction with denominator 100.
7. What does 0.52 mean in place-value language?
8. Between which two tenths does 0.37 lie?
Core
Core practice
Compare decimals and place them on a number line without treating them as whole-number strings.
9. Which is larger: 0.62 or 0.59?
10. Which is larger: 0.7 or 0.68?
11. Order from least to greatest: 0.4, 0.39, 0.42.
12. Which is smaller: 0.05 or 0.5?
13. Which is closer to 0.5: 0.47 or 0.42?
14. Is 0.76 greater or less than 3/4?
15. Give a decimal to the hundredths strictly between 0.31 and 0.33.
16. Rewrite 0.9 using hundredths.
Think
Think practice
Explain comparison errors, connect decimals to fractions, and reason about closeness.
17. A student says 0.58 > 0.6 because 58 > 6. Explain the error.
18. Which decimal equals 7/10?
19. Which fraction with denominator 100 equals 0.64?
20. How far is 0.63 from 0.60?
21. Which is larger: 0.45 or 4/10?
22. Which decimal is exactly halfway between 0.2 and 0.3?
23. Can a decimal with more digits be smaller than one with fewer digits? Give an example.
24. List three decimal names equal to one half using tenths or hundredths.
Challenge
Challenge practice
Round decimals, reason between benchmarks, and preview simple decimal equations.
25. Round 0.34 to the nearest tenth.
26. Round 0.78 to the nearest tenth.
27. Round 0.65 to the nearest tenth using the usual half-up school convention.
28. Give two decimals to the hundredths between 0.6 and 0.65.
29. Which is greater: 0.83 or 5/6? Use 5/6 ≈ 0.8333.
30. If x + 0.2 = 0.75, find x.
31. A decimal has 6 tenths, 0 hundredths, and no whole units. What is it?
32. A number rounds to 0.5 to the nearest tenth. Give one possible value to the hundredths.
Answer key
- 1. Tenths.
The first digit to the right of the decimal point is the tenths place. - 2. 7 hundredths, or 0.07.
The second digit to the right is the hundredths place. - 3. 0.6
Six tenths is 0.6. - 4. 0.23
Twenty-three hundredths is 0.23. - 5. Yes.
Four tenths equals forty hundredths. - 6. 8/100
0.08 means eight hundredths. - 7. 5 tenths and 2 hundredths.
The 5 is in the tenths place and the 2 is in the hundredths place. - 8. 0.3 and 0.4.
0.37 is 37 hundredths, which lies between 30 and 40 hundredths. - 9. 0.62
Compare tenths first: 6 tenths is greater than 5 tenths. - 10. 0.7
0.7 = 0.70, and 70 hundredths is greater than 68 hundredths. - 11. 0.39, 0.4, 0.42
Rewrite 0.4 as 0.40, then compare 39, 40 and 42 hundredths. - 12. 0.05
0.05 is five hundredths; 0.5 is fifty hundredths. - 13. 0.47
0.47 is 0.03 away from 0.50, while 0.42 is 0.08 away. - 14. Greater.
3/4 = 0.75, so 0.76 is one hundredth greater. - 15. 0.32
0.32 lies one hundredth above 0.31 and one hundredth below 0.33. - 16. 0.90
Nine tenths equals ninety hundredths. - 17. The place values are different; 0.6 = 0.60, so 60 hundredths is greater than 58 hundredths.
Whole-number comparison does not work unless decimal places are aligned. - 18. 0.7
Seven tenths is written 0.7. - 19. 64/100
0.64 means sixty-four hundredths. - 20. 0.03
63 hundredths minus 60 hundredths is 3 hundredths. - 21. 0.45
4/10 = 0.40, so 0.45 is greater. - 22. 0.25
0.25 is five hundredths above 0.20 and five hundredths below 0.30. - 23. Yes; for example, 0.08 < 0.5.
The number of written digits does not determine the value. - 24. 0.5, 0.50, and 0.500 are equal; within tenths/hundredths, 0.5 and 0.50 are the main forms.
Trailing zeros do not change a decimal’s value. - 25. 0.3
0.34 is closer to 0.3 than to 0.4. - 26. 0.8
0.78 is closer to 0.8 than to 0.7. - 27. 0.7
0.65 is exactly halfway between 0.6 and 0.7; the stated convention rounds to 0.7. - 28. For example, 0.61 and 0.64.
Any hundredths greater than 0.60 and less than 0.65 work. - 29. 5/6
About 0.8333 is slightly greater than 0.83. - 30. 0.55
0.75 - 0.20 = 0.55. - 31. 0.60, which is equal to 0.6.
Six tenths and zero hundredths can be written 0.60. - 32. For example, 0.47.
Values from 0.45 through 0.54 round to 0.5 under the usual half-up school convention.