How can we use the concept:
One real world example of standard form is expressing the speed of light in standard form. The speed of light is [299 792 458 m/s or approximately 300,000,000]. Shown in standard form the speed of light is [3 x 10⁸].
Sample Math Problems
1. Write 6.351 x 10⁷ (standard form)
Answer: [63,510,000]
Explanation: Since the decimal is located after the 6 and there are 3 spaces after the decimal, move the decimal 7 spaces to the right adding 4 zeros to fill in the spaces.
A positive exponent signals moving the decimal in the right-hand direction.
Therefore, [63,510,000] is the answer. In this whole number the decimal is “understood” to be behind the number but is not expressed in the solution.
2. Write
(standard form)
Answer: [.00000000000004806]
Explanation: Since the decimal is located after the 4 and there are 3 spaces after the decimal, move the decimal 14 spaces to the left adding 13 zeros to fill in the spaces.
A negative exponent signals moving the decimal in the left-hand direction.
Therefore, [.00000000000004806] is the answer.
A negative exponent signals moving the decimal in the left-hand direction.
Therefore, [.00000000000004806] is the answer.
3. Write
Answer: [.00000637]
Explanation: Since the decimal is located after the 6 and there are 2 spaces after the decimal, move the decimal 6 spaces to the left and add 5 zeros to fill the spaces.
A negative exponent signals moving the decimal in the left-hand direction.
Therefore, [.00000637] is the answer.
4. Write
Answer: [840,000]
Explanation: Since the decimal is located after the 8 and there is 1 space after the decimal, move the decimal 5 spaces to the right adding in 4 zeros in the spaces.
A positive exponent signals moving the decimal in the right-hand direction.
Therefore, [840,000] is the answer. In this whole number the decimal is “understood” to be behind the number but is not expressed in the solution.
