5 th Grade Powers of 10. Part I. What are powers of 10?

Size: px

Start display at page:

Download "5 th Grade Powers of 10. Part I. What are powers of 10?"

Todd Mills
5 years ago
Views:

1 5 th Grade Powers of 10 Part I. What are powers of 10? , 10, 100, 1000, 10000, etc. are all powers of 10. The fractions,,,, etc. are also considered powers of 10. In decimal form they can be written 0.1, 0.01, 0.001, , etc. 1) Of the following ten decimal numbers, five are powers of 10. Circle them. 1,000, ,000 1, Part II. Multiplying by powers of 10 like 10, 100, 1000, etc. Probably because we have ten fingers, we use a decimal system which is based on powers of 10. Because of this, it is easy to multiply and divide by powers of 10. To do so we only need to move the decimal place. To multiply a number by a power of 10 like 10, 100, or 1000, we just have to move the decimal point to the right an appropriate number of places. To multiply by 10 we move one place, to multiply by 100 we move two places, to multiply by 1000 we move three places and so on. Here are some examples: 1.25 x 10 = x 100 = x 1,000 = 1, x 1,000,000 = 1,250,000 2) Do some by yourself. 3.8 x 10 = 3.8 x 1,000 = 3.8 x 10,000,000 = 3.8 x 1 = Printed on 10/3/ of 10

2 Here are some harder examples: 1,280 x 1,000 = 1,280, x 100 = x 1,000 = 10, x 100 = 499 3) Try these. 455 x 10,000 = x 100,000 = x 10 = x 1,000 = Printed on 10/3/ of 10

3 Part III. Dividing by powers of 10 like 10, 100, 1000, etc. Dividing is just as easy; the decimal place simply moves to the left instead of to the right. Here are some examples: = = ,000 = ,000,000 = ) Do some by yourself = = ,000 = 375 1,000,000,000 = Here are some harder examples: ,000 = = , = 3,600 4,500 10,000 = ) Try these ,000 = = ,000 = ,000 = Printed on 10/3/ of 10

4 Part IV. Multiplying by powers of 10 like 0.1, 0.01, 0.001, etc. You may have noticed that so far we have only multiplied and divided by powers of 10 like 1, 10, 100, etc. In this section and the next, we will multiply and divide by powers of 10 like 0.1, 0.01, 0.001, etc. An easy way to multiply by a power of 10 like 0.1, 0.01, 0.001, etc. is to change the problem to a division problem. Look at the following examples which use the fact that for example multiplying by 0.01 (one one-hundredth) is the same as dividing by x 0.01 = = ,000 x = 75,000 1,000 = 75 8,675,309 x = 8,675, ,000 = x = 99 1,000 = ) Do some by yourself. 300 x 0.1 = 300 = 7,950 x 0.01 = 7,950 = 0.85 x = 0.85 = x = = Part V. Dividing by powers of 10 like 0.1, 0.01, 0.001, etc. Again, dividing is similar to multiplying. But, instead of changing a multiplication problem to a division problem, we change a division problem to a multiplication problem. Here are some examples: = 7.52 x 100 = = 65 x 10 = = 100 x 1,000 = 100, = x 100,000 = 1,205,000 7) Do some by yourself = 450 x = = 1.25 x = = x = = 700 x = Printed on 10/3/ of 10

5 Part VI. Multiplying and dividing summary At this point you should know how to multiply or divide by any power of ten. 8) Try these x 1,000 = x = = x 0.1 = ,000 = x = = x = = 75,250 Printed on 10/3/ of 10

6 Part VII. Unit conversion: BIG to small Conveniently, the metric system is grounded in powers of 10. This makes converting between different metric units easy. To change from BIG units to smaller units we multiply. There are: 1,000 meters in a kilometer (1,000 m in a km) 100 centimeters in a meter (100 cm in a m) 10 millimeters in a centimeter (10 mm in a cm) To convert 2.5 meters to centimeters, we have to know that there are 100 centimeters in a meter. In this case 100 centimeters per meter is called a conversion factor. 2.5 meters x 100 centimeters per meter = 250 centimeters Here are some more examples: Convert 75 kilometers to meters. 75 km x 1,000 meters per kilometer = 75,000 m Convert 2.54 centimeters to millimeters cm x 10 millimeters per centimeter = 25.4 mm Convert 0.65 meters to centimeters m x 100 centimeters per meter = 65 cm 9) Do some by yourself. Convert 0.05 kilometers to meters km x meters per kilometer = m Convert 125 centimeters to millimeters. 125 cm x = mm Convert 7.5 meters to centimeters. 7.5 m x = cm Printed on 10/3/ of 10

7 Part VIII. Unit conversion: small to BIG To change from smaller units to BIGGER units, we divide. Here are some examples: Convert 7,500 meters to kilometers. 7,500 m 1,000 meters per kilometer = 7.5 km Convert 22,000 millimeters to centimeters. 22,000 mm 10 millimeters per centimeter = 2,200 cm Convert 125 centimeters to meters. 125 cm 100 centimeters per meter = 1.25 m 10) Try these. Convert 1.6 millimeters to centimeters. 1.6 mm millimeters per centimeter = cm Convert 500 centimeters to meters. 500 cm = m Convert 800 meters to kilometers. 800 m = km Printed on 10/3/ of 10

8 Part IX. Unit conversion: summary When converting between units, one of the most important things to know is whether you need to multiply (BIG to small) or divide (small to BIG). 11) In each of the following examples, circle multiply or divide. To change millimeters to centimeters, I would multiply / divide by 10. To change meters to kilometers, I would multiply / divide by 1,000. To change meters to centimeters, I would multiply / divide by ) Fill in the blanks. To change centimeters to meters, I would: To change centimeters to millimeters, I would: Here are some examples of this process in action: Convert 55 centimeters to millimeters. 55 cm x 10 millimeters per centimeter = 550 mm Convert 300 meters to kilometers. 300 m 1,000 meters per kilometer = 0.3 km 13) Do these. Convert 86 mm to cm. Convert 5 km to m. Printed on 10/3/ of 10

9 Part X. Harder conversions Sometimes, there are conversions that are most easily done in two steps: Convert 1.5 kilometers to centimeters. 1.5 km x 1,000 meters per kilometer = 1,500 m 1,500 m x 100 centimeters per meter = 150,000 cm Convert 86,000 centimeters to kilometers. 86,000 cm 100 centimeters per meter = 860 m 860 m 1,000 meters per kilometer = 0.86 km 14) Try a few. Convert 9,500 mm to m. Convert 2.5 km to cm. Printed on 10/3/ of 10

10 Part XI. Summary Do the following problems which will test your understanding of Parts I-X. 15) Multiply or divide as indicated ,000 = 350 x 0.01 = x 10,000 = = 45 x = ,650 = ) There are 1,000 grams in a kilogram (1,000 g in a kg). There are 1,000 milligrams in a gram (1,000 mg in a g). Convert 450 grams to kilograms. Convert 450 grams to milligrams. Convert kilograms to milligrams. Printed on 10/3/ of 10

Why is math important in. healthcare?

Why is math important in. healthcare? 00 000 00 0 000 000 0 Why is math important in 00 000 00 0 000 000 0 healthcare? Health care workers are required to perform simple math calculations when doing various tasks. Mathematical errors may result