Math  /  Numbers & Operations

Question2.38×102,300,28,300%,63,2.16×1012.38 \times 10^{2}, \sqrt{300}, 2^{8}, 300 \%, 6^{3}, 2.16 \times 10^{1}
Order greatest to least

Studdy Solution

STEP 1

1. The problem involves comparing the magnitudes of various mathematical expressions.
2. Each expression must be evaluated to a numerical value before comparisons can be made.
3. The expressions include scientific notation, square roots, exponents, and percentages.

STEP 2

1. Evaluate each expression to obtain its numerical value.
2. Compare the numerical values obtained in the previous step.
3. Order the expressions from greatest to least based on their numerical values.

STEP 3

Evaluate the expression 2.38×1022.38 \times 10^2.
2.38×102=2382.38 \times 10^2 = 238

STEP 4

Evaluate the expression 300\sqrt{300}.
30017.32\sqrt{300} \approx 17.32

STEP 5

Evaluate the expression 282^8.
28=2562^8 = 256

STEP 6

Evaluate the expression 300%300\%.
300%=300×1100=3300\% = 300 \times \frac{1}{100} = 3

STEP 7

Evaluate the expression 636^3.
63=2166^3 = 216

STEP 8

Evaluate the expression 2.16×1012.16 \times 10^1.
2.16×101=21.62.16 \times 10^1 = 21.6

STEP 9

Compare all the numerical values obtained: 238238, 17.3217.32, 256256, 33, 216216, and 21.621.6.

STEP 10

Order the numerical values from greatest to least.
256,238,216,21.6,17.32,3256, 238, 216, 21.6, 17.32, 3

STEP 11

Match the ordered numerical values to their corresponding expressions.
28(256),2.38×102(238),63(216),2.16×101(21.6),300(17.32),300%(3)2^8 (256), 2.38 \times 10^2 (238), 6^3 (216), 2.16 \times 10^1 (21.6), \sqrt{300} (17.32), 300\% (3)
Therefore, the expressions in order from greatest to least are:
28,2.38×102,63,2.16×101,300,300%2^8, 2.38 \times 10^2, 6^3, 2.16 \times 10^1, \sqrt{300}, 300\%

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