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The distance from New York City to San Francisco is 2.905 x 103 miles. How does multiplying the number 2.905 by 103 change its value? New York City San Francisco In this lesson you will learn how multiplying by a power of ten increases a digit’s value by using patterns in place value. Let’s Review You can find the relationship between place values by multiplying or dividing by ten. 10 x 10 = 100 10 x 10 x . . Tenths Ones Tens 329 9 Thousandths Thousandths Hundredths Ones Hundreds Hundred Thousands Ten Thousands 941 900 Thousands Thousands Millions Ten Millions Hundred Millions Millions Let’s Review A power of ten is a special notation, called scientific notation, in which the base number is always ten. 1 10 = 10 x 1 = 10 2 1 = 10 x 10 = 100 3 0 10 = 10 x 10 x 10 = 1,000 4 10 = 10 x 10 x 10 x 10 = 10,000 5 10 = 10 x 10 x 10 x 10 x 10 = 100,000 Core Lesson When you multiply a number by a power of ten, the value of each digit increases ten times for each power. 0 4 . Thousandths . Hundredths 0 Thousandths Ones 0 Tens 0 Ones Hundreds 0 Thousands Hundred Thousands Ten Thousands Thousands Millions Ten Millions Hundred Millions Millions Tenths 4 x 10 2 3 4 5 1 Core Lesson When you multiply a number by a power of ten, the value of each digit increases ten times for each power. 1 4 x 10 = 4 x 10 = 40 2 4 x 10 = 4 x 100 = 400 3 4 x 10 = 4 x 1,000 = 4,000 4 4 x 10 = 4 x 10,000 5 = 40,000 4 x 10 = 4 x 100,000 = 400,000 Core Lesson When you multiply a number by a power of ten, the value of each digit increases ten times for each power. 0.692 x 10 Tenths Hundredths Thousandths 0 Thousandths 0 . 6 9 2 Ones Tens Ones Hundreds Thousands Hundred Thousands Ten Thousands Thousands Millions Ten Millions Hundred Millions Millions 4 15 3 2 . Core Lesson When you multiply a number by a power of ten, the value of each digit increases ten times for each power. 1 0.692 x 10 = 0.692 x 10 = 6.92 0.692 x 10 2 = 0.692 x 100 = 69.2 0.692 x 10 3 = 0.692 x 1,000 4 0.692 x 10 = 0.692 x 10,000 0.692 x 10 5 = 0.692 x 100,000 = 692. = 6,920. = 69,200. A Common Misunderstanding Thinking that you simply add a zero to the end of a number for each power you multiply by. 3 6 x 10 = 6 x 10 3 x 10 x 10 = 6,6 06 06 0 .157 x 10 = .157 x x x 10 = .157 15.7 1.57 157 10 10 3 .157 x 10 ≠ .157000 Core Lesson The distance from New York City to San Francisco is 2.905 x 103 miles. How does multiplying the number 2.905 by 103 change its value? 2.905 x 103 = 2.905 x 1,000 = 2,905 miles In this lesson you have learned how multiplying by a power of ten increases a digit’s value by using patterns in place value.