116k views
4 votes
J'von says that 8.4 times 10 to the 3rd power would equal 84000. Explain what his mistake was.

1 Answer

4 votes

Final answer:

J'von erroneously added an extra zero to the result of multiplying 8.4 by 10³, thinking it was 84000 instead of the correct answer, which is 8400.

Step-by-step explanation:

The mistake J'von made is in the interpretation of the exponent when multiplying 8.4 by 10 to the 3rd power. 10 to the 3rd power (10³) is 1000, so when we multiply 8.4 by 10³, we are multiplying 8.4 by 1000. To calculate this correctly, rather than adding three zeros to the number, we need to move the decimal point three places to the right. This gives us 8.4 * 1000 = 8400, not 84000, as J'von suggested.

This is a common issue where students might mistakenly think of 10³ as 'start with 10 and add three zeros' which would give 10,000. However, this is not correct. Each factor of 10 in 10³ represents a tenfold increase, so we only add three zeros to the digit preceding the decimal point in 8.4, resulting in 8400.

User Tom Maeckelberghe
by
7.8k points