Beyond the Point: Understanding Decimals
Decimals are another way to express parts of a whole, using place value and a decimal point to show tenths, hundredths, thousandths, and beyond. They appear everywhere in daily life β prices, measurements, sports statistics, and scientific data β making decimal literacy essential for students at every level.
Components of Understanding Decimals
This section covers the foundational concepts of decimals:
- Place Value: Each digit after the decimal point has a value β tenths (0.1), hundredths (0.01), thousandths (0.001), and so on.
- Reading & Writing Decimals: Translating between word form, expanded form, and standard decimal notation.
- Comparing & Ordering Decimals: Using place value to determine which decimal is greater or to sort a list from least to greatest.
- Rounding Decimals: Approximating a decimal to a given place value using the digit to its right.
Examples of Understanding Decimals
Place Value Examples
- In 3.47, the 4 is in the tenths place (worth 0.4) and the 7 is in the hundredths place (worth 0.07).
- In 0.285, the 2 is tenths, the 8 is hundredths, and the 5 is thousandths, totaling 2/10 + 8/100 + 5/1000.
- A measurement of 12.036 meters means 12 whole meters, 0 tenths, 3 hundredths, and 6 thousandths of a meter.
Reading & Writing Examples
- 0.75 is read as "seventy-five hundredths" or "zero point seven five."
- Write "three and four hundredths" as 3.04 β the zero holds the tenths place.
- In expanded form, 6.319 = 6 + 0.3 + 0.01 + 0.009.
Comparing & Ordering Examples
- Compare 0.6 and 0.58: Write 0.6 as 0.60, then compare hundredths β 60 hundredths > 58 hundredths, so 0.6 > 0.58.
- Order from least to greatest: 0.4, 0.38, 0.405. Rewrite as 0.400, 0.380, 0.405. The order is 0.38, 0.4, 0.405.
- A runner's times are 11.2 seconds, 11.18 seconds, and 11.205 seconds. Compare place by place: 11.18 < 11.2 < 11.205.
Rounding Examples
- Round 3.847 to the nearest tenth: Look at the hundredths digit (4). Since 4 < 5, round down to 3.8.
- Round 12.065 to the nearest hundredth: Look at the thousandths digit (5). Since 5 β₯ 5, round up to 12.07.
- A store item costs $7.349 before tax. Rounded to the nearest cent (hundredth), the price is $7.35.