Lesson 2 of 8 · Grades 4 to 5
Tenths and hundredths
A decimal point separates whole ones from parts of one. The first place after the point counts tenths and the second place counts hundredths. This lesson shows how the places work and how decimals and fractions can name the same amount.
Splitting one whole into ten
Whole numbers count whole things. Decimals count parts of a whole thing, and they start with a small dot called the decimal point. The first place after the point counts tenths. One tenth is written 0.1, and it is the same amount as the fraction 1/10.
Picture one whole as a square cut into 100 equal small squares. A tenth is a full row of 10 small squares, because 10 hundredths make one tenth.
The hundredths place
The second place after the decimal point counts hundredths. One hundredth is written 0.01, and it is the same amount as the fraction 1/100. The decimal 0.37 has a 3 in the tenths place and a 7 in the hundredths place. It names 3 tenths and 7 hundredths, which is 37 hundredths, or 37/100.
Same amount, different names
Decimals and fractions can name the same amount, and one decimal can be written in more than one way. The decimal 0.4 is 4 tenths. Because 4 tenths is the same as 40 hundredths, 0.4 = 0.40. Adding a zero at the end of a decimal does not change its value, because the extra zero says "no more hundredths".
Expanded form for decimals
Place value works on the right of the point just as it does on the left. The decimal 3.47 is 3 ones, 4 tenths and 7 hundredths, so its expanded form is 3 + 0.4 + 0.07. The chart below shows the same three digits lined up under their place names.
Watch out for this
The number of digits does not tell you the size. The decimal 0.5 is much larger than 0.05, because 0.5 is 5 tenths and 0.05 is only 5 hundredths. In the same way 0.37 is less than half of one, while 3.7 is more than three. Read the place of each digit before you decide what a decimal is worth.
Worked example
A bottle holds 2.36 litres. Write the number as a sum of ones, tenths and hundredths, then name the value of the 3.
Step 1: split the number at the decimal point. The whole part is 2.
Step 2: read the tenths place. The first digit after the point is 3, so the tenths part is 0.3.
Step 3: read the hundredths place. The second digit after the point is 6, so the hundredths part is 0.06.
Step 4: write the sum: 2 + 0.3 + 0.06. The 3 stands in the tenths place, so it is worth 0.3.
Answer: 2 + 0.3 + 0.06, and the 3 is worth 0.3.
Remember
- The decimal point separates whole ones from parts of one.
- The first place after the point is tenths: 0.1 = 1/10.
- The second place is hundredths: 0.01 = 1/100.
- Zeros at the end of a decimal do not change its value.
Try it
Answer the five questions below. Work them out first, then open each answer to check.
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Write 1/10 as a decimal.
Show answer
0.1. One tenth makes the first place after the decimal point.
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Write 0.7 as a fraction.
Show answer
7/10. The 7 is in the tenths place, so it names seven tenths.
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How many hundredths are in 0.45?
Show answer
45. The digits after the point count 45 hundredths.
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Which digit is in the tenths place of 2.63?
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6. The first place after the decimal point counts tenths.
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Write 30/100 as a decimal and as a simpler fraction.
Show answer
30/100 = 3/10 = 0.3. Thirty hundredths and three tenths name the same amount.
Puzzle · Grid hunt
Puzzle time
Each grid below is one whole split into 100 equal squares. Which grid shows 0.30 shaded?
Show a hint
0.30 means thirty hundredths, so count the shaded squares in each grid.
Show the answer
Answer: Grid A. Grid A has 30 of its 100 squares shaded, which is 0.30. Grid B shows 0.03 and Grid C shows 0.33.