Tenths and hundredths are the fractions that money and measuring use most. You know how to make equivalent fractions by multiplying; here the multiplier is always 10.
Key idea
One tenth is 10 hundredths, so $\dfrac{3}{10} = \dfrac{30}{100}$. To add tenths and hundredths, first write the tenths as hundredths: $\dfrac{3}{10} + \dfrac{4}{100} = \dfrac{30}{100} + \dfrac{4}{100} = \dfrac{34}{100}$.
Why it works
Cut a square into 10 strips: each strip is one tenth. Cut every strip into 10 small squares and the whole has 100 squares, so each strip is 10 hundredths. Three strips are 30 small squares: $\dfrac{3}{10} = \dfrac{3 \times 10}{10 \times 10} = \dfrac{30}{100}$.
Worked example: Tenths to hundredths
Fill in: $\dfrac{7}{10} = \dfrac{?}{100}$
- Each tenth is 10 hundredths.
- $7 \times 10 = 70$.
Answer: $\dfrac{70}{100}$
Worked example: Add tenths and hundredths
Find $\dfrac{6}{10} + \dfrac{25}{100}$.
- Rename: $\dfrac{6}{10} = \dfrac{60}{100}$.
- Add hundredths: $\dfrac{60}{100} + \dfrac{25}{100} = \dfrac{85}{100}$.
Answer: $\dfrac{85}{100}$
Common mistake
Adding straight across: $\dfrac{3}{10} + \dfrac{4}{100} = \dfrac{7}{110}$. Tenths and hundredths are different-size pieces, so they cannot be counted together until you rename the tenths as hundredths.