Math: Scientific Notation
Writing very large and very small numbers with powers of 10
Math: Scientific Notation
Writing very large and very small numbers with powers of 10
Math - Grade 6-8
- 1
Write 4,500 in scientific notation.
Move the decimal so the first factor is at least 1 but less than 10.
The number 4,500 in scientific notation is 4.5 x 10^3 because the decimal moves 3 places to the left. - 2
Write 0.0072 in scientific notation.
The number 0.0072 in scientific notation is 7.2 x 10^-3 because the decimal moves 3 places to the right to make 7.2. - 3
Write 8.3 x 10^5 in standard form.
A positive exponent means move the decimal to the right.
The number 8.3 x 10^5 in standard form is 830,000 because the decimal moves 5 places to the right. - 4
Write 6.1 x 10^-4 in standard form.
The number 6.1 x 10^-4 in standard form is 0.00061 because the decimal moves 4 places to the left. - 5
Write 92,000,000 in scientific notation.
The first number in scientific notation must be at least 1 but less than 10.
The number 92,000,000 in scientific notation is 9.2 x 10^7 because the decimal moves 7 places to the left. - 6
Write 0.00000045 in scientific notation.
The number 0.00000045 in scientific notation is 4.5 x 10^-7 because the decimal moves 7 places to the right. - 7
Which number is greater: 3.2 x 10^4 or 3.2 x 10^5? Explain.
Compare the exponents when the first factors are the same.
The greater number is 3.2 x 10^5 because both numbers have the same first factor, and 10^5 is 10 times larger than 10^4. - 8
Which number is smaller: 7.9 x 10^-2 or 7.9 x 10^-5? Explain.
The smaller number is 7.9 x 10^-5 because a more negative exponent means the decimal value is smaller when the first factors are the same. - 9
Write 5,670,000,000 in scientific notation.
Count how many places the decimal moves from the end of the whole number.
The number 5,670,000,000 in scientific notation is 5.67 x 10^9 because the decimal moves 9 places to the left. - 10
Write 0.00032 in scientific notation.
The number 0.00032 in scientific notation is 3.2 x 10^-4 because the decimal moves 4 places to the right. - 11
Write 1.04 x 10^6 in standard form.
Use zeros as placeholders if needed.
The number 1.04 x 10^6 in standard form is 1,040,000 because the decimal moves 6 places to the right. - 12
Write 9.8 x 10^-3 in standard form.
The number 9.8 x 10^-3 in standard form is 0.0098 because the decimal moves 3 places to the left. - 13
Is 12.4 x 10^3 written correctly in scientific notation? If not, rewrite it correctly.
Check whether the first number is at least 1 but less than 10.
No, 12.4 x 10^3 is not written correctly because the first factor must be less than 10. The correct scientific notation is 1.24 x 10^4. - 14
Is 0.6 x 10^8 written correctly in scientific notation? If not, rewrite it correctly.
No, 0.6 x 10^8 is not written correctly because the first factor must be at least 1. The correct scientific notation is 6 x 10^7. - 15
A bacterium is 0.000005 meters long. Write this length in scientific notation.
Very small numbers use negative exponents.
The length in scientific notation is 5 x 10^-6 meters because the decimal moves 6 places to the right to make 5.