Question Video: Expressing Numbers in Decimal Form Physics • 9th Grade

A block of ice is heated with 3.25 × 10⁶ J of energy. What is the number of joules of energy supplied, expressed in decimal notation?

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Video Transcript

A block of ice is heated with 3.25 times 10 to the six joules of energy. What is the number of joules of energy supplied, expressed in decimal notation?

Okay, so this question has given us an energy value, 3.25 times 10 to the power of six joules. And we’re being asked to express this number in decimal notation. Let’s begin by recalling what decimal notation actually means. A number expressed in decimal notation is written as a single number made up of integer digits in the units, tens, hundreds, thousands, et cetera positions to the left of the decimal point and possibly also in the tenths, hundredths, and so on to the right of the decimal point. For example, the number 1234.56 is expressed in decimal notation with a one in the thousands position, a two in the hundreds position, a three in the tens position, a four in the units position, a five in the tenths position, and a six in the hundredths position.

Of course, it’s also possible to have decimal numbers with further positions: ten thousands, hundred thousands, and so on to the left and thousandths, ten thousandths, et cetera to the right.

Now, the energy value we’ve been given is not currently expressed in decimal notation. Instead, this value is expressed in scientific notation. Let’s recall that a number written in scientific notation is expressed in the form 𝑎 multiplied by 10 raised to the power of 𝑏, where 𝑎 is any number that’s greater than or equal to one and less than 10 and 𝑏 is any integer value, positive or negative. In the value of energy that we’ve been given, 3.25 times 10 to the power of six joules, we can identify 3.25 as the value of 𝑎 and six as the value of 𝑏.

To rewrite this energy value in decimal notation, we need to realize that 10 to the power of six means six factors of 10 multiplied together, that is, 10 times 10 times 10 times 10 times 10 times 10. So then, 3.25 multiplied by 10 to the power of six is simply equal to 3.25 multiplied by 10 six times. Multiplying a number by 10 means moving each digit one place to the left so that the units become tens, the tens become hundreds, the hundreds become thousands, and so on. This process is completely equivalent to moving the decimal point one place to the right.

Since we’re multiplying by six factors of 10 here, we need to move the decimal point six places to the right, taking care to add in all the zeros in all the new positions to the left of the decimal point. We have found a result of 3250000 joules. This value is expressed in decimal notation, as the question asked for. Our final answer then is that the number of joules of energy supplied, expressed in decimal notation, is 3250000 joules.

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