1. Rounding Numbers
Lesson 1.4.1

2. Rounding Numbers 1.4.1 California Standard: What it means for you:
Lesson
1.4.1
Rounding Numbers
California Standard:
Mathematical Reasoning 2.1
Use estimation to verify the reasonableness of calculated results.
What it means for you:
You’ll learn about rounding exact figures to make them easier to work with.
Key words:
rounding
place value
digit
decimal
tenth
hundredth

3. Lesson
1.4.1
Rounding Numbers
Rounding involves replacing one number with another number that’s easier to work with.
9.9 × 22 = 217.8
10 × 22 = 220
“(9.9 × 22) is about 220”
You’ll use rounded numbers in the next couple of Lessons to check and to estimate answers.

4. Rounding Numbers 1.4.1 Rounded Numbers Can Be Easier To Use
Lesson
1.4.1
Rounding Numbers
Rounded Numbers Can Be Easier To Use
Suppose you wanted to find 18 × 43, but had lost your calculator. You could find an answer close to 18 × 43 by rounding to the nearest ten.
“Rounding to the nearest ten” means replacing a number with the nearest multiple of 10.
Replacing a number with a higher number is called rounding up.
Replacing a number with a lower number is called rounding down.

5. Rounding Numbers 1.4.1 Solution Next, 43:
Lesson
1.4.1
Rounding Numbers
Example 1
Round 18 and 43 to the nearest ten.
Solution
You need to decide whether to round up or down.
Look at the digit in the ones place:
If the ones digit is 5 or more, round up.
If the ones digit is 4 or less, round down.
Start with 18:
The digit in the ones place is 8.
8 is more than 5, so round up.
18 rounded up to the nearest ten is 20.
Next, 43:
The digit in the ones place is 3.
3 is less than 4, so round down.
43 rounded down to the nearest ten is 40.
Solution follows…

6. Lesson
1.4.1
Rounding Numbers
By rounding, you can replace 18 × 43 with 20 × 40.
This is much easier to solve: 20 × 40 = 800
800 is fairly close to the real answer: 18 × 43 = 774

7. Rounding Numbers 1.4.1 Guided Practice
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 1–8, round the numbers to the nearest ten.
1. 36
3. 199
5. 267 40
2. 84 80
200
4010
270
7160
2990
3000
9. During a science experiment, a group of students observed that there were 415 ants in a colony. Round this amount to the nearest ten.
420
Solution follows…

8. Rounding Numbers 1.4.1 You Can Round to Different Place Values
Lesson
1.4.1
Rounding Numbers
You Can Round to Different Place Values
You can round numbers to place values other than tens.
Write the number.
35,926
21,337
Underline the digit in the position you want to round to.
21,337
35,926
If the digit to the right of the underlined digit is 5 or more, round up.
35,926
21,337
21,300
36,000
If the digit to the right of the underlined digit is 4 or less, round down.

9. Lesson
1.4.1
Rounding Numbers
Example 2
Round 25,281 to the nearest hundred.
Solution
Write the number and underline the hundreds digit:
25,281
You’re rounding to the nearest hundred, so that’s going to be either 25,200 or 25,300.
The digit to the right of the underline is 8.
That’s greater than 5, so round up.
25,300
So 25,281 rounds up to 25,300, to the nearest hundred.
Solution follows…

10. Rounding Numbers 1.4.1 Guided Practice
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 10–13, round the numbers to the nearest hundred.
10. 38,383
13. 40,079
38,400
5800
8100
40,100
Solution follows…

11. Rounding Numbers 1.4.1 Guided Practice
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 14–17, round the numbers to the nearest thousand.
14. 11,905
16. 2,599,582
,333
12,000
8000
2,600,000
464,000
18. Clara lives in a city that has a population of 82,458 people. Write this population rounded to the nearest thousand.
82,000
Solution follows…

12. Rounding Numbers 1.4.1 You Can Round Decimals Just Like Whole Numbers
Lesson
1.4.1
Rounding Numbers
You Can Round Decimals Just Like Whole Numbers
You round decimals in the same way as whole numbers.
Instead of rounding to the nearest ten, hundred, and so on, you round to the nearest one, tenth, hundredth, or any other number of decimal places.
0.746
0.746
0.75

13. Lesson
1.4.1
Rounding Numbers
Example 3
Round to the nearest thousandth.
Solution
Write the number and underline the thousandths digit:
0.0815
The nearest thousandth will be either or
Look to the right of the underline.
The digit to the right is 5, so round up.
0.082
So rounds up to 0.082, to the nearest thousandth.
Solution follows…

14. Rounding Numbers 1.4.1 Guided Practice
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 19–22, round the numbers to the nearest tenth.
28.1
2.2
5.8
6.9
Solution follows…

15. Rounding Numbers 1.4.1 Guided Practice
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 23–26, round the numbers to the nearest hundredth.
0.11
15.60
409.49
7.73
Solution follows…

16. Rounding Numbers 1.4.1 Guided Practice
Lesson
1.4.1
Rounding Numbers
Guided Practice
In Exercises 27–30, round the numbers to the nearest thousandth.
9.461
1.725
5.227
3.101
Solution follows…

17. Rounding Numbers 1.4.1 Guided Practice
Lesson
1.4.1
Rounding Numbers
Guided Practice
31. A distance of 1 mile is equal to km. Write this to the nearest hundredth of a kilometer.
1.61 km
Exercises 32–34 are about Malik, who has $ in his pocket.
32. How much money does Malik have to the nearest dollar?
33. How much money does Malik have to the nearest dime?
34. How much money does Malik have to the nearest quarter?
$13.00
$12.60
$12.50
Solution follows…

18. Rounding Numbers 1.4.1 Independent Practice
Lesson
1.4.1
Rounding Numbers
Independent Practice
In Exercises 1–5, round the number 94, :
1. to the nearest hundred
2. to the nearest hundredth
3. to the nearest thousandth
4. to the nearest thousand
5. to the nearest one
94,500
94,521.84
94,
95,000
94,522
Solution follows…

19. Rounding Numbers 1.4.1 Independent Practice
Lesson
1.4.1
Rounding Numbers
Independent Practice
6. The number 3478 was rounded to To what place value was the number rounded?
Tens
7. Raul’s thermometer shows that the temperature is 91.5 °F. What is the temperature to the nearest degree?
92 °F
8. Mount Whitney is 14,505 feet high. Write this figure to the nearest hundred feet.
14,500 feet
Solution follows…

20. Rounding Numbers 1.4.1 Independent Practice
Lesson
1.4.1
Rounding Numbers
Independent Practice
9. The average distance from the Earth to the Moon is 238,857 miles. What is this distance to the nearest thousand miles?
239,000 miles
10. The speed of light is 299,792,458 meters per second. What is this to the nearest million m/s?
300,000,000 m/s
11. Jessica has $ What is this amount to the nearest quarter?
$17.25
12. A square inch is equal to cm². Convert 6 in² to cm², then round your answer to the nearest hundredth.
38.71 cm2
Solution follows…

21. Rounding Numbers 1.4.1 Round Up
Lesson
1.4.1
Rounding Numbers
Round Up
Rounding numbers makes them easier to deal with. You can use rounded numbers to quickly find an approximate answer when you don’t need an exact one.
They can also help you to check your work, by letting you get an idea of how big your answer should be.