Video: Using Scientific Notation to Estimate Large and Small Quantities

The ship Titanic that sank in the Atlantic had a mass of about 47450000 kg. Which one of the following could be used as an estimate for this value? [A] 5 × 10⁶ [B] 5 × 10⁷ [C] 5 × 10⁸ [D] 4 × 10⁷ [E] 4 × 10⁸

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Video Transcript

The ship Titanic that sank in the Atlantic had a mass of about 47450000 kilogrammes. Which one of the following could be used as an estimate for this value? Is it A) five multiplied by 10 to the power of six? B) Five multiplied by 10 to the power of seven? C) Five multiplied by 10 to the power of eight? D) Four multiplied by 10 to the power of seven? Or E) four multiplied by 10 to the power of eight?

Our five answers are all written in scientific notation in the form 𝑎 multiplied by 10 to the power of 𝑏. We know that they’re in scientific notation as the absolute value of 𝑎 is less than 10 and greater than or equal to one. The value of 𝑏 is an integer. We need to convert 47450000 kilogrammes into scientific notation and then see which of our answers is the best estimate.

In order to write a number in scientific notation, we begin by finding the first nonzero digit. In this question, it is a four. We put a decimal point after this number and then write all the other nonzero digits. In this case, we have 4.745. This will be multiplied by 10 to some power. The exponent will be positive when dealing with large numbers and negative when dealing with small numbers. In this case, it will be a positive integer.

We need to work out how many times we would multiply 4.745 by 10 to get the answer 47450000. We can do this using place value or by counting the number of times the decimal point would move to the right. In this case, the answer is seven. 47450000 written in standard form is 4.745 multiplied by 10 to the power of seven. Looking at our five possible answers, we can immediately see that options A, C, and E are incorrect as the exponent is not seven.

In order to round our value of 𝑎, 4.745, to the nearest integer, we look at the number in the tenths column. As this is a seven, we will round up. So, our estimate becomes five multiplied by 10 to the power of seven. The correct answer is B, an estimate of 47450000 kilogrammes is five multiplied by 10 to the power of seven kilogrammes.

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