3 Decimals
Decimal notation is based on powers of 10: 0.1 is one tenth, 0.01 is one hundredth, 0.001 is one thousandth, and so on.
| thousands | hundreds | tens | ones/units | . | tenths | hundredths | thousandths |
Exercises
- ninety and twenty-three hundredths
- seven and fifty-six thousandths
Adding & Subtracting Decimals
Before you add or subtract decimals, you must line up the decimal points.
Exercises
- 3.75 + 12.8
- 71.085 + 112.93
When subtracting, you may need to add zeros to the first number so you can borrow correctly.
Exercises
- 46.57 − 38.29
- 82.78 − 67.024
Multiplying Decimals
To multiply decimal numbers:
- Temporarily ignore the decimal points.
- Multiply the numbers as though they are whole numbers.
- Add the total number of decimal digits in the two numbers you multiplied. The result will have that number of digits to the right of the decimal point.
Note: You do NOT need to line up the decimal points when you are multiplying.
Exercises
- 143 ∙ 29
- 143 ∙ 2.9
- 14.3 ∙ 2.9
- 1.43 ∙ 2.9
- 375 ∙ 175
- 375 ∙ 0.175
- 3.75 ∙ 1.75
- Evie worked 37.5 hours at a pay rate of $17.50 per hour. How much did she earn in total?
Dividing Decimals
Let’s review everyone’s favorite topic, long division. The three parts of a division are named as follows: dividend ÷ divisor = quotient. When this is written with a long division symbol, the dividend is inside the symbol, the divisor is on the left, and the quotient is the answer we create on top.
To divide by a decimal:
- Write in long division form.
- Move the decimal point of the divisor until it is a whole number.
- Move the decimal point of the dividend the same number of places to the right.
- Place the decimal point in the quotient directly above the decimal point in the dividend.
- Divide the numbers as though they are whole numbers.
- If necessary, add zeros to the right of the last digit of the dividend to continue.
Exercises
- 974 ÷ 4
- 974 ÷ 0.4
- 9,740 ÷ 0.04
- 0.0974 ÷ 0.004
Rounding Numbers
It is often necessary to round a number to a specified place value. We will see more specific instructions in Modules 5 & 6, but let’s review the basics of rounding a number.
Rounding a number:
- Locate the rounding digit in the place to which you are rounding.
- Look at the test digit directly to the right of the rounding digit.
- If the test digit is 5 or greater, increase the rounding digit by 1 and drop all digits to its right.
- If the test digit is less than 5, keep the rounding digit the same and drop all digits to its right.
Exercises
- 6,375 (thousands)
- 6,375 (tens)
- 0.7149 (hundredths)
- 0.7149 (thousandths)
If a decimal answer goes on and on, it may be practical to round it off.
Exercises
- A subscription to The Chicago Manual of Style Online costs $44.00. Determine the monthly cost, rounded to the nearest cent.
- In the summer of 1919, a military convoy (including Lt. Col. Dwight Eisenhower) drove from Washington, D.C. to San Francisco to assess the condition of the nation’s developing highway system. The journal entry for August 1 says “Good dirt roads. Made 82 miles in 11 hrs.”[1] What was the convoy’s effective speed in miles per hour for that day? Round your result to the nearest tenth.
- Source: https://after-ike.com/logbook-1919-transcontinental-military-convoy/. See https://www.nytimes.com/2019/07/07/opinion/the-most-important-road-trip-in-american-history.html if you're interested in the historical context. ↵
