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Comparing & Estimating with Scientific Notation — Easy Worksheet 1
Grade 8 · MathSheets Name: ____________________ Date: __________
Answer each question. Write standard-form answers without commas.
How to solve
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Example
Which number is greater: 7.3 × 105 or 7.6 × 105?
Answer: 7.6 × 105
Not quite. The answer is
💡 Compare the powers of 10 first: 11 > 9, so 1011 is bigger than 109. Both decimal parts are between 1 and 10, so the larger power wins: 7.1 × 1011 is greater.
✓ Correct!
Not quite. The answer is
💡 Compare the powers of 10 first: 11 > 9, so 1011 is bigger than 109. Both decimal parts are between 1 and 10, so the larger power wins: 7.1 × 1011 is greater.
💡 How to solve: Comparing & Estimating with Scientific Notation
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Try a similar one
Which number is greater: 3.7 × 109 or 1.1 × 109?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Divide the larger number by the smaller one. Divide the decimal parts: 8 ÷ 4 = 2. Subtract the exponents: 3 − 2 = 1. So it is 2 × 101 = 20 times as large. The answer is 20.
✓ Correct!
Not quite. The answer is
💡 Divide the larger number by the smaller one. Divide the decimal parts: 8 ÷ 4 = 2. Subtract the exponents: 3 − 2 = 1. So it is 2 × 101 = 20 times as large. The answer is 20.
💡 How to solve: Comparing & Estimating with Scientific Notation
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Try a similar one
Which number is greater: 8.9 × 107 or 8.8 × 107?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The exponent is 3, so move the decimal point 3 places to the right, filling empty places with zeros. 3.3 × 103 = 3300.
✓ Correct!
Not quite. The answer is
💡 The exponent is 3, so move the decimal point 3 places to the right, filling empty places with zeros. 3.3 × 103 = 3300.
💡 How to solve: Comparing & Estimating with Scientific Notation
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Try a similar one
Which number is greater: 1.2 × 105 or 5.4 × 105?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 First write it in scientific notation: 6,690,000 = 6.69 × 106. Round 6.69 to the nearest whole number: 7. So 6,690,000 ≈ 7 × 106.
✓ Correct!
Not quite. The answer is
💡 First write it in scientific notation: 6,690,000 = 6.69 × 106. Round 6.69 to the nearest whole number: 7. So 6,690,000 ≈ 7 × 106.
💡 How to solve: Comparing & Estimating with Scientific Notation
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Try a similar one
Which number is greater: 4.2 × 109 or 6.6 × 109?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Compare the powers of 10 first: 4 > 3, so 104 is bigger than 103. Both decimal parts are between 1 and 10, so the larger power wins: 5.4 × 104 is greater.
✓ Correct!
Not quite. The answer is
💡 Compare the powers of 10 first: 4 > 3, so 104 is bigger than 103. Both decimal parts are between 1 and 10, so the larger power wins: 5.4 × 104 is greater.
💡 How to solve: Comparing & Estimating with Scientific Notation
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Try a similar one
Which number is greater: 2.6 × 107 or 6.6 × 105?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 Divide the larger number by the smaller one. Divide the decimal parts: 4 ÷ 2 = 2. Subtract the exponents: 6 − 4 = 2. So it is 2 × 102 = 200 times as large. The answer is 200.
✓ Correct!
Not quite. The answer is
💡 Divide the larger number by the smaller one. Divide the decimal parts: 4 ÷ 2 = 2. Subtract the exponents: 6 − 4 = 2. So it is 2 × 102 = 200 times as large. The answer is 200.
💡 How to solve: Comparing & Estimating with Scientific Notation
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Try a similar one
Which number is greater: 9.6 × 103 or 4.9 × 102?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 The exponent is 5, so move the decimal point 5 places to the right, filling empty places with zeros. 9.7 × 105 = 970000.
✓ Correct!
Not quite. The answer is
💡 The exponent is 5, so move the decimal point 5 places to the right, filling empty places with zeros. 9.7 × 105 = 970000.
💡 How to solve: Comparing & Estimating with Scientific Notation
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Try a similar one
Which number is greater: 7.3 × 108 or 7.4 × 106?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 First write it in scientific notation: 9,450,000 = 9.45 × 106. Round 9.45 to the nearest whole number: 9. So 9,450,000 ≈ 9 × 106.
✓ Correct!
Not quite. The answer is
💡 First write it in scientific notation: 9,450,000 = 9.45 × 106. Round 9.45 to the nearest whole number: 9. So 9,450,000 ≈ 9 × 106.
💡 How to solve: Comparing & Estimating with Scientific Notation
Compare the powers of 10 first — the larger exponent is the larger number; if the exponents match, compare the decimal parts. To find how many times as large, divide the decimal parts and subtract the exponents: (6 × 108) ÷ (2 × 105) = 3 × 103 = 3000.
Try a similar one
Which number is greater: 1.9 × 109 or 1.2 × 1011?
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Comparing & Estimating with Scientific Notation — Easy Worksheet 1
Answer each question. Write standard-form answers without commas.