Rounding Quotients: Homework

Divide, find the place you are rounding to, and ask what the answer is FOR. A bill rounds up; a batting average rounds to the nearest.

Part A — Divide and Round / 10

Divide, then round to the place asked.

Each of these has a trap. Ask what the answer is for before you round.

1.
5 ÷ 9. Round it to the nearest hundredth. Then cut it off at the hundredths without rounding. Are the two answers the same?Answer
2.
Six friends share a $20 snack bill equally, and each must pay enough to cover it. What does each pay?Answer
3.
50 students need rides, and each van seats 8. 50 ÷ 8 = 6.25. How many vans?Answer
4.
A student rounds 2 ÷ 3 to 0.6 for the tenths place. What went wrong?Answer
5.
Which skill? Round 8.3333 to the nearest hundredth. Then split a $50 bill among 6 friends, each paying enough to cover it. Do both answers match? Why or why not? (Rounding a decimal is U2-L2. Rounding a quotient is U2-L8.)Answer

Real numbers. A batting average is hits divided by at bats. A speed is distance divided by time.

1.
Two of the best batting seasons in baseball. Round each average to the nearest thousandth.
Player, year Hits At bats
Ted Williams, 1941 185 456
Tony Gwynn, 1994 165 419
a. Williams: hits ÷ at batsAnswer
b. Gwynn: hits ÷ at batsAnswer
c. How much higher was Williams's average than Gwynn's, using the rounded numbers?Answer
2.
Usain Bolt's world records, set in Berlin in 2009: 100 meters in 9.58 seconds and 200 meters in 19.19 seconds. Speed is meters divided by seconds.
a. His speed in the 100 meters, to the nearest hundredth of a meter per second.Answer
b. His speed in the 200 meters, to the nearest hundredth.Answer
c. To the nearest tenth, are the two speeds different? Which race was a little faster?Answer

Player, year	Hits	At bats
Ted Williams, 1941	185	456
Tony Gwynn, 1994	165	419

Think it through, then write your answer and one sentence about how you knew.

1.
Write a division of two whole numbers whose quotient, rounded to the nearest tenth, is the SAME as the quotient cut off at the tenths. Then write one where they are different.Answer
2.
Name one situation where a quotient must be rounded UP, and one where you round to the NEAREST. Write a division for each.Answer

Write your own, then work it.

1.
Write a money problem where dividing gives a decimal that does not end, and the share must be rounded UP to the cent. Solve it and show why rounding down would be wrong.Answer

Total / 24

Graded by

Notes

Part A — the rounded quotients.

Part B — the answer.

0.56 rounded, but 0.55 cut off. They are different, because the digit next door is 5.
$3.34. The nearest cent is $3.33, but six of those make $19.98, short by 2 cents, so the bill rounds UP.
7 vans. 6 vans seat only 48, so you round UP.
0.7. 2 ÷ 3 = 0.666..., and the 6 next door is 5 or more, so it rounds up. Cutting it off at 0.6 is not rounding.
8.33 for the plain decimal. But the bill is 50 ÷ 6 = 8.3333..., and 6 × 8.33 = 49.98 is short, so each friend pays $8.34. The bill rounds up.

Part C — the answers.

a. 0.406 b. 0.394 c. 0.012
a. 10.44 meters per second b. 10.42 meters per second c. 10.4 and 10.4, the same to the nearest tenth. But hundredths show the 100 meters was a little faster.

Part D — one correct answer, and what a good explanation says.

Answers vary. 1 ÷ 3 = 0.333..., and both give 0.3. But 7 ÷ 9 = 0.777..., which rounds to 0.8 and cuts off to 0.7. They match when the digit next door is 0 to 4.
Answers vary. Up: vans, boxes, or a bill that must be covered, such as 45 ÷ 4 vans. Nearest: an average or a measurement, such as a batting average of 185 ÷ 456.

Part E — what a good problem looks like.

Answers vary. A good one checks that the rounded shares cover the bill, such as $10 shared by 3: each pays $3.34, because 3 × $3.33 = $9.99 is a cent short.