Final answer:
In mathematics, particularly at the middle school level, division of fractions involves multiplying the first fraction by the reciprocal of the second. For operations involving powers of tens, subtract the exponent in the denominator from the exponent in the numerator to simplify the expression.
Step-by-step explanation:
To compute the division of 1093/19864 by 1937/10937, one can perform a multiplication by the reciprocal of the second fraction. The calculation can be carried out as follows:
- Convert the division into a multiplication: (1093/19864) × (10937/1937).
- Multiply the numerators together: 1093 × 10937.
- Multiply the denominators together: 19864 × 1937.
- Divide the product of the numerators by the product of the denominators to get the result.
Similarly, when dividing by powers of 10, the exponents are subtracted. Additionally, in expressions like 2.4 × 10¹³ divided by 8 × 10⁷, the powers of ten are managed by subtracting the exponent of the denominator from the exponent of the numerator, resulting in 2.4 × 10⁶ after accounting for division by 8.
Understanding these principles can make division involving fractions and scientific notation more straightforward without the need for a calculator.