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.
