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Math
Decimals
Understanding Tenths and Hundredths
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Decimals show parts of a whole by using place value to the right of the decimal point. The first place after the decimal point is tenths, and the second place is hundredths. This helps us describe amounts that are between whole numbers, such as money, measurements, and points on a number line. Understanding tenths and hundredths makes it easier to compare, add, and subtract decimal numbers.
Key Facts
- In 1.34, the 1 means 1 one, the 3 means 3 tenths, and the 4 means 4 hundredths.
- 1 tenth = 0.1 = 1/10.
- 1 hundredth = 0.01 = 1/100.
- 10 hundredths = 1 tenth, so 0.10 = 0.1.
- 1.34 = 1 + 0.3 + 0.04 = 1 + 3/10 + 4/100.
- To compare decimals, line up the decimal points and compare digits from left to right.
Vocabulary
- Decimal
- A decimal is a number that uses a decimal point to show whole number parts and fractional parts.
- Tenths
- Tenths are one of ten equal parts of a whole and are written in the first place to the right of the decimal point.
- Hundredths
- Hundredths are one of one hundred equal parts of a whole and are written in the second place to the right of the decimal point.
- Place value
- Place value is the value of a digit based on its position in a number.
- Decimal point
- The decimal point separates the whole number part from the fractional part of a decimal.
Common Mistakes to Avoid
- Reading 1.34 as one point thirty-four without understanding place value. The 3 means 3 tenths and the 4 means 4 hundredths, not 34 whole units.
- Thinking 0.4 is smaller than 0.34 because 4 has fewer digits. This is wrong because 0.4 = 0.40, and 40 hundredths is greater than 34 hundredths.
- Forgetting to line up decimal points when adding or subtracting. Digits must be placed in matching place-value columns, such as ones under ones and tenths under tenths.
- Believing that adding a zero at the end changes the value of a decimal. A zero at the end after the decimal does not change the value, so 0.5 = 0.50.
Practice Questions
- 1 Write 2.47 in expanded form using ones, tenths, and hundredths.
- 2 Which is greater, 0.6 or 0.58? Explain using hundredths.
- 3 A model shows one whole square shaded, three tenths shaded, and four hundredths shaded. Explain why the decimal is 1.34.