Math  /  Numbers & Operations

QuestionConvert each of the numbers from real to scientific notation. (17) 196.12 (24) 0.00017853 (18) 508.8 1.9612×1021.9612 \times 10^{2} \qquad (19) 0.0005024 (20) 3,949 (21) 0.005909 (22) 938,900 (23) 1.118 (25) 1,237.91,237.9 (26) 1.452 (27) 2.976 (28) 0.101 (29) 0.02417 (30) 4,557 Copyright (c2012 WorksheetWorks.com

Studdy Solution

STEP 1

1. Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form.
2. A number is written in scientific notation when it is expressed as a×10n a \times 10^n , where 1a<10 1 \leq a < 10 and n n is an integer.

STEP 2

1. Identify the decimal point position.
2. Move the decimal point to create a new number between 1 and 10.
3. Count the number of places the decimal point was moved to determine the exponent.
4. Write the number in scientific notation.

STEP 3

Identify the decimal point position for each number.

STEP 4

Move the decimal point to create a new number between 1 and 10 for each number.

STEP 5

Count the number of places the decimal point was moved to determine the exponent for each number.

STEP 6

Write the number in scientific notation.
Let's convert each number:
(17) 196.12: - Move the decimal 2 places to the left: 1.9612×102 1.9612 \times 10^2 .
(24) 0.00017853: - Move the decimal 4 places to the right: 1.7853×104 1.7853 \times 10^{-4} .
(18) 508.8: - Move the decimal 2 places to the left: 5.088×102 5.088 \times 10^2 .
(19) 0.0005024: - Move the decimal 4 places to the right: 5.024×104 5.024 \times 10^{-4} .
(20) 3,949: - Move the decimal 3 places to the left: 3.949×103 3.949 \times 10^3 .
(21) 0.005909: - Move the decimal 3 places to the right: 5.909×103 5.909 \times 10^{-3} .
(22) 938,900: - Move the decimal 5 places to the left: 9.389×105 9.389 \times 10^5 .
(23) 1.118: - The decimal is already between 1 and 10: 1.118×100 1.118 \times 10^0 .
(25) 1,237.9: - Move the decimal 3 places to the left: 1.2379×103 1.2379 \times 10^3 .
(26) 1.452: - The decimal is already between 1 and 10: 1.452×100 1.452 \times 10^0 .
(27) 2.976: - The decimal is already between 1 and 10: 2.976×100 2.976 \times 10^0 .
(28) 0.101: - Move the decimal 1 place to the right: 1.01×101 1.01 \times 10^{-1} .
(29) 0.02417: - Move the decimal 2 places to the right: 2.417×102 2.417 \times 10^{-2} .
(30) 4,557: - Move the decimal 3 places to the left: 4.557×103 4.557 \times 10^3 .

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