7th Grade Math

186 Rational Numbers

Express Small Numbers in Standard Form

Express 5.8 × 10 –^3 in standard form.

5.8 × 10 –^3 = 5.8 × 0.001 10 –^3 = 0.001

= 0.0058 Move the decimal point 3 places to the left.

c. 4.7 × 10 –^5 d. 9 × 10 –4

To write a number in scientific notation, place the decimal point after

the first nonzero digit. Then find the power of 10.

Express Numbers in Scientific Notation

Express each number in scientific notation.

1,457,000

1,457,000 = 1.457 × 1,000,000 The decimal point moves 6 places to the left.

= 1.457 × 106 The exponent is positive.

0.00063

0.00063 = 6.3 × 0.0001 The decimal point moves 4 places to the right.

= 6.3 × 10 -^4 The exponent is negative.

e. 35,000 f. 0.00722

Compare the exponents to compare numbers in scientific notation.

With positive numbers, any number with a greater exponent is

greater. If the exponents are the same, compare the factors.

Compare Numbers in

Scientific Notation

OCEANS The Atlantic Ocean has an area of 3.18 × 107 square

miles. The Pacific Ocean has an area of 6.4 × 107 square miles.

Which ocean has the greater area?

3.18 < 6.4 3.18 × 107 < 6.4 × 107

So, the Pacific Ocean has the greater area.

g. Replace  with <, >, or = to make 4.13 × 10 –^2  5.0 × 10 –^3

a true sentence.

Move the Decimal Point Move the Decimal Point

The exponent tells you how

many places to move the

decimal point.

• If the exponent is positive,
  move the decimal point
  to the right.


• If the exponent is
  negative, move the
  decimal point to the left.

Real-World Link

At the deepest point

in the ocean, the

pressure is greater

than 8 tons per

square inch and the

temperature is only a

few degrees above

freezing.

RR

A

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