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LEARNING GOALS
By the end of this lesson, you should understand
- The purpose of rounding numbers.
By the end of this lesson, you should be able to
- Round whole numbers and decimals to a specified place value.
FUNDAMENTALS OF THE LESSON
Rounding is a key and necessary skill in mathematics, as calculations often result in decimal numbers that have many digits before and after the decimal point. To round effectively, you must consider the context (or purpose) of the calculation. This will help you identify the appropriate number of decimal places to round to.
1. Let’s begin by identifying digits within numbers that are in specific decimal places.
A. 547 Determine the digit in the hundreds place.
B. 476,542 Determine the digit in the thousands place.
C. 26,573,000,000 Determine the digit in the billions place.
D. 782,956,400 Determine the digit in the hundreds thousands place.
E. 372.84 Determine the digit in the tens place.
F. 17.435 Determine the digit in the tenths place.
G. 3.1459 Determine the digit in the hundredths place.
H. 0.03468 Determine the digit in the thousandths place.
2. Given the numbers below, identify the decimal place that each digit of the number is in.
A. The number 2,154,900 is shown in the table below. Write the place values that correspond to each digit. For example, 9 is in the hundreds place, so write Hundreds into the box below the 9 digit.
| 2 | 1 | 5 | 4 | 9 | . | ||
| Decimal point |
B. The number 76.5438 is shown in the table below. Write the place values that correspond to each digit.
| 7 | 6 | . | 5 | 4 | 3 |
| Decimal point |
Rounding with the Number Line
Brianna and Rosa live in New York State and are thinking about moving to Ohio. In looking at the two states spending on education, Brianna found that New York was planning to spend $13.1 billion in 2018. Rosa found that Ohio is planning to spend $10,682,738,002. They found it difficult to compare those two numbers so they decided to round them both to the nearest billion.
3. A. Place 13.1 billion on the number line below:
B. Which billion marker is 13.1 billion nearest to?
C. We can now say that 13.1 billion rounded to the nearest billion is ____________ billion.
D. Now place $10,682,738,002 on the number line below:
E. Which billion marker is $10,682,738,002 nearest to?
F. We can now say that $10,682,738,002 rounded to the nearest billion is ____________ billion.
G. Now compare the two states’ spending on education, using your prior answers.
The number line is helpful for rounding numbers. However, it would be useful to have a way to round without having to draw the line. Complete the following examples and then come up with a rule that you can use to round without using the number line.
4. A. Round 3,721,900 to the nearest million. The location of 3,271,900 is displayed on the number line below.
3,721,900 rounded to the nearest million is __________________________________
B. Round 582,478 to the nearest thousand. The location of 582,478 is displayed on the number line below.
582,478 rounded to the nearest thousand is __________________________________
C. What is a rule (strategy) for rounding a number to a specific decimal place that does not involve using the number line? Check that the strategy works for questions 4A and 4B.
5. Let’s see if the rule you identified works for rounding to places less than one (tenths, hundredths, etc). Jorge is going to Mexico and uses a website to find out that 1 Mexican peso = 0.0548521 US dollars. He wants to round that to the hundredths place (cents).
A. Using the number line, which number, rounded to the nearest hundredth, is 0.0548521 nearest to? ________________________
B. 0.0548521 rounded to the nearest hundredths is __________________________
6. Jorge’s friend suggests an additional trip into Belize. Jorge finds that 1 Belizean dollar = 0.0496315 US dollars. Jorge uses the number line to round 0.0496315 to the hundredths place:
A. Using the number line, which number, rounded to the nearest hundredth, is 0.0496315 nearest to? ________________________
B. 0.0496315 rounded to the nearest hundredths is __________________________
C. Does your rule from Question 4 work with decimal places also? Do you need to change the way you worded it? If so, write the new rule below.
7. Use the general rule of rounding to round the numbers below.
A. Round 23,495,000 to the nearest million: _______________________
B. Round 5,890 to the nearest thousand: ___________________________
C. Round 5.728 to the nearest hundredth (this is also called “rounding to two decimal places” ) ______________________________
D. Round 0.7236 to the nearest tenth (this is also called “rounding to one decimal place”) _________________________________
E. Round 5.6666666 to one decimal place: _______________________________
F. Round 7.3449 to two decimal places: __________________________________
FURTHER APPLICATIONS
When performing calculations, you sometimes have to determine on your own the number of decimal places to round to. To do so, you can use the situation to help you make this decision. For example, if you are determining the number of people you want to invite to a party, the number you get should be a whole number. It would not make sense to invite 6.73 people to a party. Sometimes you can round a solution to a problem based on how the numbers that you were given in the problem were rounded.
8. For each problem below, think about the situation, and then round the numbers as you deem appropriate.
A. Maya is selling T-shirts with her own designs. She buys 70 plain T-shirts for $400. How much did each one cost her?
B. Remember that Ohio was planning to spend about $11 billion ($11,000,000,000) on education. Ohio has 1,729,916 children in its public schools. About how much are they planning to spend on each child? Round to the nearest dollar.
C. A school district has 5,942 students. The district’s budget for school lunches is $16,950. How much money are they spending per student?
9. Julius is trying to find out which is smaller: \(\dfrac{1}{13}\) or \(\dfrac{2}{27}\). One way to do this is to change both fractions to decimals.Use your calculator to divide the numerator (top number) by the denominator (bottom number). Do this for both fractions. Which fraction, \(\dfrac{1}{13}\) or \(\dfrac{2}{27}\), is smaller?
Questions: Rounding
1. Round 78,381,818 to the nearest million.
2. Round 650,414 to the nearest hundred thousand.
3. Round 46.276 to the nearest tenth.
4. Round 1.333333333 to one decimal place.
5. Round 0.03626 to two decimal places.
6. Round 51.812% to the nearest tenth of a percent.
7. Round 19.59% to the nearest percent.
8. In a recent year, Americans owed approximately $1,510,290,000,000 in student loan debt, spread out among about 44 million borrowers. Round $1,510,290,000,000 to the nearest hundred billion.
9. Many college students graduate college with student loan debt. One student owed $32,056 in student loan debt. Round $32,056 to the nearest thousand.
10. Sarah’s student loan debt increased by 5.3106% from 2016 to 2017. Round 5.3106% to the nearest tenth of a percent.
