Section A: Practice Problems Measurement Conversions and Powers of 10

Section Summary

Details

In this section we studied powers of 10 and conversions between units. We learned that we can write a product of 10s like $10 \times 10 \times 10 \times 10$ as $10^{4}$ . The number 4 is an exponent and it means that there are 4 factors of 10.

We also converted between different measurement units, mostly metric lengths. For example, there are 1,000 millimeters in a meter and 1,000 meters in a kilometer. This means that there are $1, 000 \times 1, 000$ or $1, 000, 000$ millimeters in a kilometer. We could also say that there are $10^{6}$ millimeters in a kilometer. We also used our understanding of decimals to make conversions. For example, since there are 1,000 meters in a kilometer that means that each meter is $\frac{1}{1, 000}$ or 0.001 kilometers. So 853 meters can also be written as 0.853 kilometers.

Problem 1 (Pre-Unit)

Find the number that makes each equation true. Explain or show your reasoning.

$\frac{}{12} = \frac{2}{3}$
$\frac{5}{6} = \frac{}{12}$

Problem 2 (Pre-Unit)

The road around a lake is 15 kilometers long. How many meters is that?
The length of an alligator is 4 meters. How many centimeters is that?

Problem 3 (Pre-Unit)

The value of the 6 in 618,204 has how many times the value as the 6 in 563? Explain or show your reasoning.

Problem 4 (Pre-Unit)

Find the value of each sum.

$\frac{3}{8} + \frac{9}{8}$
$3 \frac{1}{5} + \frac{3}{5}$
$2 \frac{4}{10} + 1 \frac{7}{10}$

Problem 5 (Pre-Unit)

Lin spent 5 minutes reading the story. Noah spent 3 times as long as Lin. How long did Noah spend reading the story? Explain or show your reasoning.

Problem 6 (Pre-Unit)

Write a multiplication expression for the shaded area and find the value of the expression. Explain or show your reasoning.
Find the value of $\frac{5}{7} \times \frac{10}{3}$ .

Problem 7 (Pre-Unit)

The line plot shows the lengths of some toothpicks in inches.

Dot plot titled Toothpick Measurements from 0 to 3 by 1’s.

How many measurements are there?
What is the difference between the longest and shortest toothpicks?

Problem 8 (Lesson 1)

Write a multiplication equation relating the values of 0.5 and 0.05.
Write a division equation relating the values of 0.5 and 0.05.

Problem 9 (Lesson 2)

Write each number using exponential notation.

$10 \times 10 \times 10$
$100 \times 100$
100,000
1,000,000,000

Problem 10 (Lesson 3)

How many centimeters are in each measurement?

0.12 m

3.5 m

19 m
How many millimeters are in each measurement?

3 m

37 m

1,915 m
How does a whole number of meters change when it is converted to millimeters?

Problem 11 (Lesson 4)

How many meters are in each measurement?

16 millimeters

1,375 millimeters

57 millimeters
How does a whole number of millimeters change when you express the measurement in meters?

Problem 12 (Lesson 5)

A track is 366 meters around. An athlete runs 15 laps. How many kilometers is that? Explain or show your reasoning.

Problem 13 (Lesson 6)

Clare drinks 8 glasses of water each day. There are 235 milliliters in each glass. How many liters of water does Clare drink each day? Explain or show your reasoning.

Problem 14 (Lesson 7)

A track is 400 yards around. How many full laps does Tyler need to run if he wants to run at least 2 miles?

Problem 15 (Exploration)

Write each of these numbers using exponential notation.

1,000,000,000 (the approximate population of Africa in 2009)
100,000,000,000 (estimated number of stars in Milky Way)
1,000,000,000,000 (amount of dollars added to United States debt each year recently)
100,000,000,000,000 (denomination of a bill in Zimbabwe)
1,000,000,000,000,000,000,000 (estimated number of stars in universe)
10,000,000,000,000,000,000 (estimated number of grains of sand on the earth)
100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000 (estimated number of atoms in the universe!)
How is exponential notation helpful for writing these numbers?

Problem 16 (Exploration)

You have a piggy bank with 1 kg of coins inside. Which coins would you like to be in the piggy bank? Explain or show your reasoning.

coin	approximate weight (grams)
penny	$2.5$
nickel	$5$
dime	$2.3$
quarter	$5.7$