Decimals (Intro)
Tenths, Hundredths & Place Value
A decimal shows parts of a whole using a decimal point. The first digit after the point is tenths (0.1 = 1/10) and the second is hundredths (0.01 = 1/100).
In 3.45 there are 3 ones, 4 tenths and 5 hundredths. So 3.45 = 3 + 0.4 + 0.05.
Example 1: Write 7 tenths as a decimal.
7 tenths = 0.7.
Example 2: In 2.45, what does the digit 4 stand for?
4 is in the tenths place, so it stands for 0.4 (four-tenths).
Quick recap
- First decimal place = tenths; second = hundredths.
- 0.1 = 1/10 and 0.01 = 1/100.
✓ Quick check
What does 0.3 mean?
0.3 is 3 tenths.
In 5.62, the digit 2 is in the ___ place.
The second digit after the point is hundredths.
Fractions to Decimals & Comparing
A fraction with denominator 10 or 100 is easy to write as a decimal: 3/10 = 0.3 and 45/100 = 0.45. Also ½ = 5/10 = 0.5.
To compare decimals, compare the whole-number part first, then the tenths, then the hundredths. So 0.5 is greater than 0.45 because 5 tenths beats 4 tenths.
Example 1: Write ½ as a decimal.
½ = 5/10 = 0.5.
Example 2: Which is bigger, 0.7 or 0.65?
0.7 = 0.70, and 70 hundredths > 65 hundredths, so 0.7 is bigger.
Quick recap
- Denominator 10 → one decimal place; 100 → two places.
- Compare wholes, then tenths, then hundredths.
✓ Quick check
Write 7/10 as a decimal.
7/10 = 0.7.
Which is greater, 0.8 or 0.08?
0.8 is 8 tenths, far bigger than 0.08 (8 hundredths).
Adding & Subtracting Decimals
To add or subtract decimals, line up the decimal points so tenths sit under tenths and hundredths under hundredths, then add or subtract as usual.
For example, 0.5 + 0.25 = 0.75, and 2.5 − 1.25 = 1.25.
Example 1: Add 0.6 + 0.3.
0.6 + 0.3 = 0.9.
Example 2: Subtract 2.5 − 1.25.
Line up points: 2.50 − 1.25 = 1.25.
Quick recap
- Line up the decimal points before adding or subtracting.
- Fill missing places with zeros if needed (2.5 = 2.50).
✓ Quick check
What is 0.45 + 0.25?
0.45 + 0.25 = 0.70.
What is 1.0 − 0.4?
1.0 − 0.4 = 0.6.
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