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Help! Compare the following: 1) 5.8 × 10^-5 and 6.2 × 10^-6 2) 3.45 × 10^5 and 0.34 × 10^6 3) 22.8 × 10^-9 and 0.058

Help! Compare the following: 1) 5.8 × 10^-5 and 6.2 × 10^-6 2) 3.45 × 10^5 and 0.34 × 10^6 3) 22.8 × 10^-9 and 0.058 × 10^-7 (2) The order of a certain natural number is 6. How many digits does the decimal representation of this number contain?
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  • Виталий_2192
    Виталий_2192
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    Comparing Numbers in Scientific Notation:
    When comparing numbers in scientific notation, it's important to consider both the coefficient and the exponent. Let's compare the given numbers step by step:

    1) To compare 5.8 × 10^-5 and 6.2 × 10^-6, first, we compare the coefficients: 5.8 and 6.2. Since 6.2 is greater than 5.8, we know that 6.2 × 10^-6 is greater than 5.8 × 10^-5.

    2) For 3.45 × 10^5 and 0.34 × 10^6, again we compare the coefficients: 3.45 and 0.34. Since 3.45 is greater than 0.34, we can conclude that 3.45 × 10^5 is greater than 0.34 × 10^6.

    3) Comparing 22.8 × 10^-9 and 0.058 × 10^-7, we compare the coefficients once again: 22.8 and 0.058. As 22.8 is greater than 0.058, we can determine that 22.8 × 10^-9 is greater than 0.058 × 10^-7.

    (2) Number of Digits in Decimal Representation:
    To find the number of digits in the decimal representation of a number, we can use the formula: log10(number) + 1. Given that the order of the natural number is 6 (meaning it has 6 digits), we can calculate the number of digits in the decimal representation as log10(10^6) + 1 = 6 + 1 = 7.

    Задание:
    Calculate and compare the following numbers in scientific notation:

    1) 8.6 × 10^4 and 7.3 × 10^3
    2) 2.5 × 10^6 and 3.8 × 10^5
    3) 0.004 × 10^-2 and 0.25 × 10^-3
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