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Why all the NOISE?!

So, basically the photography of the baby is underexposured and a underexposure photo make as much noise as a high iso one. Despite this, as has been said, a old sensor like the D3000 produce much noise even in low ISO like 800 or 1600. The D3300, for exemple, is much better in this regard.
Try to use fast lenses too, like the 35mm f/1.8g. It help a lot when you need to make indoor shots.
 
If you're using your camera/lens near their maximum capabilities you need to nail the exposure if you want to minimize noise.

As mentioned the photo of the child is badly under exposed.
You do not say what metering mode you used, nor if when you added ISO so you could speed up the shutter if you added sufficient ISO.

If you added 2 stops of shutter speed, you needed to add 2 stops of ISO to keep the exposure the same.
If the light meter in the camera is indicating under exposure you have needed to add a 3rd stop of ISO.

In case you don't know what a 'stop' is and how it relates to the triad of exposure adjustments.
A Stop
A stop is a fundamental photography concept.

A 'stop' is a doubling (2x) or a halving (0.5x) of the amount of light that reaches the recording media, be it film or an electronic sensor.
A stop change in exposure can apply to shutter speed, lens aperture, and/or ISO.

Since exposure is a triad of adjustments (shutter speed, ISO, lens aperture) you can change 1, 2 or all 3 of the triad settings.

If you want 1 more stop of exposure (brighter) you can adjust just one of the 3 by 1 more stop.
Or, you can change 2 of the 3 by 1/2 more stop each for a net gain of 1 stop of exposure.
Or, you can adjust all 3 by 1/3 more stop for a net gain of 1 stop of exposure.

You can also change the triad of settings and have no change in the exposure.

If you change 1 of the 3 settings by 1 stop more exposure and change a 2nd setting by 1 stop less exposure the net change is zero.

Suppose you subtracted a stop of shutter speed to help stop subject motion, you could add a stop of lens aperture to keep the exposure the same. However, adding a stop of aperture will also affect the total DoF by a small amount. So, if you don't want the DoF to change you would add a stop of ISO instead, however, adding a stop of ISO will increase by some amount the image noise in the photo.

Note: DSLR cameras are set by default to adjust the exposure settings in 1/3 stop increments.
Most DSLR cameras let you change that to 1/2 stop or 1 stop increments.
However, the advantage of 1/3 stop step increments is more precise control of exposure.
 
Well, thats one of the reasons why I love using a modern "full frame" (small format, 36x24mm, Nikon calls it "FX") like the Nikon D600 - you can often go to ISO 6400 with little pain. My old D5100 can go up to ISO 1400 without general pain. Depends upon the subject though, some ISO 4000 images still looked pretty okay, and of course theres always grayscale mode (iirc Nikon calls it monochrome) to help out.

Combine that with a nice prime like one of the "cheap" f1.8 ones and photographing in very low light is quite possible.

Larger sensors and brighter lenses will help with lowlight.


I had actually JUST added my first low aperture lens to my cart the other day so hopefully that will help,
Well, from context people will understand you correctly, but for the record, you will probably confuse people a lot less if you would say something like "wide aperture" or "low f-number".

Because what you call "low aperture" means a low f-number which means a *large*, not low, aperture, i.e. the lens will have a large aperture opening and collect a lot of light.

For example a 35mm f1.8 lens will have an aperture opening of 35mm / 1.8 ~ 19.4mm (diameter).
 
You need a 50mm 1.8. The noise in my D90 eventually inspired me to go full frame, but this great crop frame camera really came to life once I got my first low aperture lens. The 35mm 1.8 was an amazing investment as well.
 
I shoot with a Nikon D3000, which I know is some-what of the more mediocre Nikon models.
I know a lot of Canon users who are able to photograph indoors with no use of flash & their images look great, simply by cranking up the ISO. However, anytime I turn my ISO past 200 I get so much noise and I HATE it. Do other Nikon models offer less noise? Is there some special trick I don't know about to prevent the noise?

I actually dug this photo up for another thread, but here's an image that was shot at ISO 6400 on a Nikon D5100:

https://farm6.staticflickr.com/5497/11142749833_f21f909042_k.jpg

The 5100's actually do a pretty good job of noise reduction overall, so if you are thinking of going with a newer camera body you really wouldn't have to invest a ton of money to step up a lot in noise reduction. I'd actually recommend a used D5200, they are a fantastic value for the money and the sensor is even better than the one in the 5100.
 
50mm 1.8D will go a long ways with this issue....that and adding some light.
 

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